The following table gives the distribution of students of two sections according to the marks obtained by them:
Marks (Section $A$) Frequency (Section $A$) Marks (Section $B$) Frequency (Section $B$)
$0-10$ $3$ $0-10$ $5$
$10-20$ $9$ $10-20$ $19$
$20-30$ $17$ $20-30$ $15$
$30-40$ $12$ $30-40$ $10$
$40-50$ $9$ $40-50$ $1$

Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons,compare the performance of the two sections.

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(N/A) We can find the class marks of the given class intervals by using the following formula:
$\text{Class mark} = \frac{\text{Upper class limit} + \text{Lower class limit}}{2}$
Marks Class mark Frequency (Section $A$) Frequency (Section $B$)
$0-10$ $5$ $3$ $5$
$10-20$ $15$ $9$ $19$
$20-30$ $25$ $17$ $15$
$30-40$ $35$ $12$ $10$
$40-50$ $45$ $9$ $1$

By plotting the class marks on the $x$-axis and frequency on the $y$-axis,we draw the frequency polygons for both sections.
From the graph,it can be observed that the frequency polygon for section $A$ is shifted more towards the right compared to section $B$. This indicates that the students of section $A$ have performed better than the students of section $B$ in terms of obtaining higher marks.

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Similar Questions

The lengths of $40$ leaves of a plant are measured correct to one millimetre,and the obtained data is represented in the following table:
Length (in $mm$) Number of leaves
$118-126$ $3$
$127-135$ $5$
$136-144$ $9$
$145-153$ $12$
$154-162$ $5$
$163-171$ $4$
$172-180$ $2$

$(i)$ Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]
$(ii)$ Is there any other suitable graphical representation for the same data?
$(iii)$ Is it correct to conclude that the maximum number of leaves are $153 \, mm$ long? Why?

The following table gives the life times of $400$ neon lamps:
The time (in hours) Number of lamps
$300-400$ $14$
$400-500$ $56$
$500-600$ $60$
$600-700$ $86$
$700-800$ $74$
$800-900$ $62$
$900-1000$ $48$

$(i)$ Represent the given information with the help of a histogram.
$(ii)$ How many lamps have a life time of more than $700$ hours?

Find the mode of $14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.$

The value of $\pi$ up to $50$ decimal places is given below:
$3.14159265358979323846264338327950288419716939937510$
$(i)$ Make a frequency distribution of the digits from $0$ to $9$ after the decimal point.
$(ii)$ What are the most and the least frequently occurring digits?

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$100$ surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
Number of letters Number of surnames
$1-4$ $6$
$4-6$ $30$
$6-8$ $44$
$8-12$ $16$
$12-20$ $4$

$(i)$ Draw a histogram to depict the given information.
$(ii)$ Write the class interval in which the maximum number of surnames lie.

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